1. **State the problem:** Two resistors with resistances $5\ \Omega$ and $7\ \Omega$ are connected in series to a $60$-volt source. We need to find the power absorbed by the $5\ \Omega$ resistor. 2. **Formula and rules:** When resistors are in series, the total resistance $R_{total}$ is the sum of individual resistances: $$R_{total} = R_1 + R_2$$ The current $I$ through the series circuit is given by Ohm's law: $$I = \frac{V}{R_{total}}$$ Power absorbed by a resistor is: $$P = I^2 R$$ 3. **Calculate total resistance:** $$R_{total} = 5 + 7 = 12\ \Omega$$ 4. **Calculate current through the circuit:** $$I = \frac{60}{12} = 5\ \text{amperes}$$ 5. **Calculate power absorbed by the $5\ \Omega$ resistor:** $$P = I^2 R = 5^2 \times 5 = 25 \times 5 = 125\ \text{watts}$$ **Final answer:** The power absorbed by the $5\ \Omega$ resistor is $125$ watts.